Siegfried Beckus, Tobias Hartnick, Felix Pogorzelski
Published 2020-01-29Version 1
We show that linearly repetitive Delone sets in Heisenberg groups have a uniquely ergodic hull. More generally we establish unique ergodicity of hulls of weighted Delone sets in amenable unimodular lcsc groups under a new repetitivity condition which we call tempered repetitivity, and which coincides with linear repetitivity for certain metrics on groups of polynomial growth. Our proof is based on a new general sub-additive convergence theorem, which also has applications concerning the existence of certain Banach densities and uniform approximation of the spectral distribution function of finite hopping range operators on Cayley graphs.
Linear repetitivity, I. Uniform subadditive ergodic theorems and applications
Substitution Dynamical Systems: Characterization of Linear Repetitivity and Applications
On the existence of ergodic automorphisms in ergodic ${\mathbb Z} ^d$-actions on compact groups
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